Combobox with button instead of textbox

I would like to create a combobox without any textbox and with a customizable icon in the button that op开发者_运维知识库ens the combobox. Something like this image (forget about the checkboxs)

I don't need you to post the solution, just some directions or resources so I can know how to begin this customization.

TIA

ContextMenuStrip which you manually display in the button's Click handler.